Properties

Label 1332.2.q
Level 13321332
Weight 22
Character orbit 1332.q
Rep. character χ1332(529,)\chi_{1332}(529,\cdot)
Character field Q(ζ6)\Q(\zeta_{6})
Dimension 7676
Newform subspaces 11
Sturm bound 456456
Trace bound 00

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Defining parameters

Level: N N == 1332=223237 1332 = 2^{2} \cdot 3^{2} \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1332.q (of order 66 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 333 333
Character field: Q(ζ6)\Q(\zeta_{6})
Newform subspaces: 1 1
Sturm bound: 456456
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M2(1332,[χ])M_{2}(1332, [\chi]).

Total New Old
Modular forms 468 76 392
Cusp forms 444 76 368
Eisenstein series 24 0 24

Trace form

76q2q3+q7+2q94q11+3q153q216q2364q2523q279q29+6q31+16q3318q355q3712q39+12q41+6q43+3q45++44q99+O(q100) 76 q - 2 q^{3} + q^{7} + 2 q^{9} - 4 q^{11} + 3 q^{15} - 3 q^{21} - 6 q^{23} - 64 q^{25} - 23 q^{27} - 9 q^{29} + 6 q^{31} + 16 q^{33} - 18 q^{35} - 5 q^{37} - 12 q^{39} + 12 q^{41} + 6 q^{43} + 3 q^{45}+ \cdots + 44 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(1332,[χ])S_{2}^{\mathrm{new}}(1332, [\chi]) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
1332.2.q.a 1332.q 333.k 7676 10.63610.636 None 1332.2.q.a 00 2-2 00 11 SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Decomposition of S2old(1332,[χ])S_{2}^{\mathrm{old}}(1332, [\chi]) into lower level spaces

S2old(1332,[χ]) S_{2}^{\mathrm{old}}(1332, [\chi]) \simeq S2new(333,[χ])S_{2}^{\mathrm{new}}(333, [\chi])3^{\oplus 3}\oplusS2new(666,[χ])S_{2}^{\mathrm{new}}(666, [\chi])2^{\oplus 2}